Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20283631 | C2 | semidirect |
| 3. #20276423 | C2 | semidirect |
| 4. #20275614 | C2 | semidirect |
| 5. #20272829 | C2 | semidirect |
| 6. #20272803 | C2 | semidirect |
| 7. C2×C53×#359 | C2 | semidirect |
| 10. #16811064 | C4 | semidirect |
| 12. #16811059 | C4 | semidirect |
| 177. C2×#359 | D53 | semidirect |
| 209. C53 | #13021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287849 | 2 |
| #20283631 | 2 |
| #20276423 | 2 |
| #20275614 | 2 |
| #20272829 | 2 |
| #20272803 | 2 |
| C2×C53×#359 | 2 |
| #13021 | 53 |